The possibility of matter coupling to two metrics at once is considered. This appears natural in the most general ghost-free, bimetric theory of gravity, where it unlocks an additional symmetry with ...respect to the exchange of the metrics. This double coupling, however, raises the problem of identifying the observables of the theory. It is shown that if the two metrics couple minimally to matter, then there is no physical metric to which all matter would universally couple, and that moreover such an effective metric generically does not exist even for an individual matter species. By studying point particle dynamics, a resolution is suggested in the context of Finsler geometry.
In this paper we consider an extended Gauss-Bonnet gravity theory in arbitrary dimensions and in a space provided with a Weyl connection, which is torsion-free but non-metric-compatible, the ...non-metricity tensor being determined by a vector field. The action considered consists of the usual Einstein-Hilbert action plus all the terms quadratic in the curvature that reduce to the usual Gauss-Bonnet term for vanishing Weyl connection, i.e., when only the Levi-Civita part of the connection is present. We expand the action in terms of Riemannian quantities and obtain vector-tensor theories. We find that all the free parameters only appear in the kinetic term of the vector field, so two branches are possible: one with a propagating vector field and another one where the vector field does not propagate. We focus on the propagating case. We find that in four dimensions, the theory is equivalent to Einstein's gravity plus a Proca field. This field is naturally decoupled from matter, so it represents a natural dark matter candidate. Also for d = 4, we discuss a non-trivial cubic term in the curvature that can be constructed without spoiling the second-order nature of the field equations, because it leads to the vector-tensor Horndeski interaction. In arbitrary dimensions, the theory becomes more involved. We show that, even though the vector field presents kinetic interactions which do not have symmetry, there are no additional propagating degrees of freedom with respect to the usual massive case. We show that, interestingly, this relies on the fact that the corresponding Stückelberg field belongs to a specific class within the general Horndeski theories. Finally, since Weyl geometries provide the natural ground on which to build scale invariant theories, we apply the usual Weyl gauging in order to make the Horndeski action locally scale invariant, and discuss new terms that can be added.
General parallel cosmology Aguiar Gomes, Débora; Beltrán Jiménez, Jose; Koivisto, Tomi S.
Journal of cosmology and astroparticle physics,
12/2023, Letnik:
2023, Številka:
12
Journal Article
Recenzirano
Odprti dostop
Abstract
General (tele)parallel Relativity, G
∥
R, is the relativistic completion of Einstein's theories of gravity. The focus of this article is the derivation of the homogeneous and isotropic ...solution in G
∥
R. The first-principles derivation, based on a non-trivial realisation of the symmetry, supersedes and unifies previous constructions of Riemannian and teleparallel cosmologies, and establishes the uniqueness of the physical solution. The constitutive law and the form of the material and inertial source currents is presented in the tensor (Palatini) formalism and adapted to the cosmological background, which exhibits novel features absent in the previously studied, static solutions to the theory. The results are contrasted with those in incomplete theories, such as sitting at the three corners of the geometrical trinity which correspond to particular reference frames in G
∥
R.
Listening to Celestial Algebras Beltrán Jiménez, Jose; Koivisto, Tomi S.
Universe (Basel),
08/2022, Letnik:
8, Številka:
8
Journal Article
Recenzirano
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In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. ...Remarkably, they permit interesting non-trivial realisations of the cosmological principle with an interplay between the symmetry groups of the quaternions and octonions. We also argue how these realisations give rise to potentially observational signatures in gravitational waves astronomy.
Abstract
In this work we study diffeomorphism-invariant metric-affine theories of gravity from the point of view of self-interacting field theories on top of Minkowski spacetime (or other ...background). We revise how standard metric theories couple to their own energy-momentum tensor, and discuss the generalization of these ideas when torsion and nonmetricity are also present. We review the computation of the corresponding currents through the Hilbert and canonical (Noether) prescriptions, emphasizing the potential ambiguities arising from both. We also provide the extension of this consistent self-coupling procedure to the vielbein formalism, so that fermions can be included in the matter sector. In addition, we clarify some subtle issues regarding previous discussions on the self-coupling problem for metric theories, both General Relativity and its higher derivative generalizations. We also suggest a connection between Lovelock theorem and the ambiguities in the bootstrapping procedure arising from those in the definition of conserved currents.
Inflation from N-forms and its stability Koivisto, Tomi S; Mota, David F; Pitrou, Cyril
The journal of high energy physics,
09/2009, Letnik:
2009, Številka:
9
Journal Article
Three-form cosmology Koivisto, Tomi S.; Nunes, Nelson J.
Physics letters. B,
03/2010, Letnik:
685, Številka:
2-3
Journal Article
Recenzirano
Odprti dostop
Cosmology of self-interacting three-forms is investigated. The minimally coupled canonical theory can naturally generate a variety of isotropic background dynamics, including scaling, possibly ...transient acceleration and phantom crossing. An intuitive picture of the cosmological dynamics is presented employing an effective potential. Numerical solutions and analytical approximations are provided for scenarios which are potentially important for inflation or dark energy.
The no-hair theorem postulates that the only externally observable properties of a black hole are its mass, its electric charge, and its angular momentum. In scalar-tensor theories of gravity, a ...matter distribution around a black hole can lead to the so called 'spontaneous scalarisation' instability that triggers the development of scalar hair. In the Brans-Dicke type theories, this effect can be understood as a result of tachyonic effective mass of the scalar field. Here we consider the instability in the generalised class of scalar-theories that feature non-conformal, i.e. 'disformal', couplings to matter. Such theories have gained considerable interest in the recent years and have been studied in a wide variety of systems, both cosmological and astrophysical. In view of the prospects of gravitational wave astronomy, it is relevant to explore the implications of the theories in the strong-gravity regime. In this article, we concentrate on the spontaneous scalarisation of matter configurations around Schwarzschild and Kerr black holes. We find that in the more generic scalar-tensor theories, the instability of the Brans-Dicke theory can be enhanced, suggesting violations of the no-hair theorem. On the other hand, we find that, especially if the coupling is very strong, or if the gradients in the matter distribution are negligible, the disformal coupling tends to stabilise the system.
Cosmology of hybrid metric-Palatini f ( X )-gravity Capozziello, Salvatore; Harko, Tiberiu; Koivisto, Tomi S ...
Journal of cosmology and astroparticle physics,
04/2013, Letnik:
2013, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed a la Palatini was proposed recently. The ...dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity X = Kappa super(2)T + R, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure.
Coincident general relativity Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi
Physical review. D,
08/2018, Letnik:
98, Številka:
4
Journal Article
Recenzirano
Odprti dostop
The metric-affine variational principle is applied to generate teleparallel and symmetric teleparallel theories of gravity. From the latter we discover an exceptional class which is consistent with a ...vanishing affine connection. Based on this remarkable property, this work proposes a simpler geometrical formulation of general relativity that is oblivious to the affine spacetime structure, thus fundamentally depriving gravity of any inertial character. The resulting theory is described by the Hilbert action purged from the boundary term and is more robustly underpinned by the spin-2 field theory, where an extra symmetry is now manifest, possibly related to the double-copy structure of the gravity amplitudes. This construction also provides a novel starting point for modified gravity theories, and the paper presents new and simple generalizations where analytical self-accelerating cosmological solutions arise naturally in the early- and late-time Universe.
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